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math.SP2026
A sandwich theorem for the spectrum of graph coverings
Charles Bordenave, Wenbo Li, Joe Thomas
We show that all normal covers of a fixed finite graph sitting between the universal and maximal abelian covers share the same atomic part of their spectral measures. We give a…
math.SP2025
Eigenvalues of Maximal Abelian Covers
Wenbo Li, Michael Magee, Mostafa Sabri +1
We fully characterize the eigenvalues (flat bands) of the maximal abelian cover of a finite multi-graph in terms of the combinatorics of the base graph. This solves a problem of Hi…